U.S. GDP grew by 3.5% in the third quarter of 2009. That was a bigger increase from the third quarter of 2008 than the 3.2% that the majority of economists had been expecting. This marks the first time that the economy has grown after four straight quarters of contraction.

The number is probably—probably—strong enough to give new impetus to the rally that began on March 9 and that has been going through a very modest correction in the last week and a half. If you’re a bull who believes that the economy has entered a sustainable recovery, this report will give you reason for renewed confidence in that scenario.

But the report won’t quiet those—myself included—who worry about the “sustainable” part of that recovery scenario. Too much of the growth in the third quarter came from government stimulus to make me confident that the economy would keep rolling once that stimulus ends.

Now on to the numbers.

The good news was everywhere in this report.

Consumption climbed 3.4%. Gross private domestic investment was up 11.5%. Exports increased by 14.7%. Imports grew by 16.4%

All together that’s a picture of a growing economy.

But all isn’t quite as rosy if you dig a little deeper. Much of this growth came from spending driven by the federal government’s stimulus programs.

In the auto sector, Cash for Clunkers, boosted car sales and that in turn added a little over one percentage point to the 2.4 percentage points that personal consumption added to the final GDP number.

The $8,000 tax-credit for first time home buyers had a similar effect on construction activity. Residential construction jumped at a 23 percent annual rate in the third quarter. That’s the first increase in almost four years. The jump in construction activity added about half a percentage point to growth.

Those of us who believe the economy isn’t out of the woods yet got more to worry about in the weekly unemployment claims report issued the same morning as the GDP numbers. Initial claims, that’s the number of workers filing new claims for unemployment, held steady at 530,000 workers. Continuing claims, that’s the number of workers who were on unemployment and who continued to receive unemployment benefits, fell to 5.797 million from 5.945 million the week before.

Those numbers aren’t as positive as they seem on first look. New claims for unemployment aren’t sinking at the kind of sustained rate we need if overall unemployment is going to fall. In fact, it looks now like initial claims have settled into a range between 525,000 and 535,000. That’s better than the range of 550,000 to 600,000 in the summer months, but a range above 500,000 isn’t going to reduce unemployment.

The continued claims number is completely misleading. The decline is a result of dithering in the Senate about extending unemployment benefits. This recession has gone on for so long that about 7,000 workers lose their benefits each day because they have been unemployed too long. Without Senate action about 1.3 million workers will drop out of the continued claims number by December.

I’ve seen the quotes from Wall Street bulls calling this a complete and total confirmation of the sustainable recovery scenario. And I’ve seen the crowing saying that the fourth quarter will be Waterloo for the bears.

I’m glad to see the enthusiasm. It does indeed suggest that the trend is still upward.

But I don’t think this is any time to get carried away. As anyone who reads military history knows, Waterloo was a very, very near thing.